The large deviations principle (LDP) is known to hold for U-statistics of real valued kernel functions of Polish space valued i. i. d. random variables, where moreover appropriate exponential tail conditions are assumed to hold. We prove that similar conditions suuce for the large deviations principle to carry over to the partial sums U-processes corresponding to the statistics. x1 Introduction...

In this paper, we simulate different types of random fuzzy variables to get some conclusions concerning fuzzy-valued random variables. This simulation has been carried out to illustrate certain limit results formalizing the convergence of the arithmetic mean of sample fuzzy data to the population mean (or expected value of the random fuzzy variable), like the well-known strong law of large numb...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described by K is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’...

The Ginibre ensemble of nonhermitean random Hamiltonian matrices K is considered. Each quantum system described by K is a dissipative system and the eigenenergies Zi of the Hamiltonian are complex-valued random variables. The second difference of complex eigenenergies is viewed as discrete analog of Hessian with respect to labelling index. The results are considered in view of Wigner and Dyson’...

Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...